Complex Fuzzy Rough Sets and Their Applications

This book explains the foundational principles of fuzzy algebra, including fuzzy sets, fuzzy operations, and fuzzy relations. It shows how fuzzy algebra can be applied in artificial intelligence, particularly in areas such as decision-making, pattern recognition, and machine learning, where uncertainty and imprecision are common. It demonstrates the use of fuzzy algebra in engineering disciplines, such as control systems, cybersecurity, signal processing, and robotics, where fuzzy logic can be used to model and solve complex and real-world problems. This makes the book valuable not just for process engineers, but also for researchers in multiple domains.

This book is designed to familiarize data science, machine learning and other engineering professionals, in a relatively simple and easy to understand fashion, with decision making skills founded on calculations and case study based quantitative analysis.

Tahir Mahmood is an associate professor of Mathematics at the Department of Mathematics and Statistics, International Islamic University Islamabad, Pakistan. He received his Ph.D. degree in Mathematics from Quaid-i-Azam University Islamabad, Pakistan in 2012 in the field of Fuzzy Algebra. His areas of interest are algebraic structures, fuzzy algebraic structures, decision making and generalizations of fuzzy sets. Around 360 research publications are on his credit with more than 10,500 citations, 850 impact factor, 50 h-index and around 200 i10-index. He has produced 63 M.Sc. students and 9 Ph.D. students.  Currently he is working as an editorial board member of 3 impact factor journals and as editor-in-chief of the journal “Journal of Innovative Research in Mathematical and Computational Sciences.”

Jabbar Ahmmad received his M.Sc., M.Sc. and Ph.D. degrees in Mathematics from International Islamic University Islamabad, Pakistan, in 2018, 2020, and 2024, respectively. His research interests include fuzzy sets and their generalizations, fuzzy algebraic structures, aggregation operators, similarity measures, fuzzy decision-making, rough sets, soft sets, decision-making theory, and machine learning. He has published more than 35 articles in well-reputed peer-reviewed journals.

Ubaid ur Rehman is working as an assistant professor at the Department of Mathematics, University of Management and Technology, Lahore, Pakistan. He received his Ph.D. degree in Mathematics from the International Islamic University Islamabad, Pakistan in 2023. His research interests include fuzzy sets and their generalizations, aggregation operators, similarity measures, fuzzy decision-making, rough sets, soft sets, decision-making theory, and artificial intelligence. He has published more than 80 articles in well-reputed peer-reviewed journals with 250+ impact factor. He has been a member of the academic board of Global Open Share Publishing since 2024.

Harish Garg is working as an associate professor at Thapar Institute of Engineering & Technology, Patiala, Punjab, India. He received the Most Outstanding Researcher award in the field of Mathematics from Carrer 360 Academy. He is also the recipient of the International Obada-Prize 2022 – Young Distinguished Researchers. He is also the recipient of the Top-Cited paper by an India-based author (2015–2019) from Elsevier Publishers. He also serves as an advisory board member of the Universal Scientific Education and Research Network (USERN). He is a research fellow at INTI International University, Malaysia. He is ranked in the World’s Top 2% Scientist List and Rank #1 in India & World Rank #163 published by Stanford University in the consecutive years from 2020-2024. Dr. Garg’s research interests include computational intelligence, multi-criteria decision making, evolutionary algorithms, reliability analysis, expert systems and decision support systems, computing with words and soft computing. He has authored more than 540 papers (over 520 are SCI) published in refereed international journals including IEEE Transactions, Elsevier, Springer, etc. His Google citations are over 28,300 with H-index of 93. He is one of the leading researchers in the world related to the reliability, MCDM and soft computing approaches. Dr. Garg also serves on editorial boards of several leading international journals, this includes the founding editor-in-chief of the Journal of Computational and Cognitive Engineering. He is also the associate editor of Alexandria Engineering Journal, Journal of Industrial & Management Optimization, CAAI Transactions on Intelligence Technology, etc.